AMApplied Mathematics2152-7385Scientific Research Publishing10.4236/am.2014.51006AM-41613ArticlesPhysics&Mathematics Note on the Linearity of Bayesian Estimates in the Dependent Case ouadAssoudou1*BelkheirEssebbar2Department of Mathematics and Computer Sciences, Faculty of Science, Mohammed V University, Rabat, MoroccoDepartment of Economics, Faculty of Law, Economics and Social Sciences, Hassan I University, Settat, Morocco* E-mail:s_assoudou@yahoo.fr(OA);2512201305014754September 21, 2013October 21, 2013 October 28, 2013© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

This work deals with the relationship between the Bayesian and the maximum likelihood estimators in case of dependent observations. In case of Markov chains, we show that the Bayesian estimator of the transition probabilities is a linear function of the maximum likelihood estimator (MLE).

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